What is the equation of the line passing through

Question

(0, 2) and perpendicular to the line y = 4x – 3 in slope-intercept form?

Answer 1

The given line equation is y = 4x -3

The general slope - intercept form is y = mx+c

Therefore slope m = 4

Any perpendicular line slope is - 1/m = -1/4

The slope intercept form of line equation is

y = mx+c

Substitute x = 0, y = 2 and m = -1/4 in above equation

2 = (-1/4)(0)+c

2 = c

Therefore c = 2

Substitute m and c value in equation y = mx+c

y =( -1/4)x+2

The solution is y =( -1/4)x+2.

 

Answer 2

Slope - intercept form line equation is y = mx + b, where m is slope and b is y - intercept.

The line is y = 4x - 3. and the point is (0, 2).

Compare the line with slope - intercept form.

Slope (m) = 4.

Because the slopes of perpendicular lines are negative reciprocals, the slope of perpendicular is - 1/4.

Now, the perpendecular line equation is y = (- 1/4)x + b.

Find the y - intercept by substituting the point in the perpendecular line equation say (x, y) = (0, 2).

2 = (- 1/4)(0) + b

⇒ b = 2.

The perpendecular line equation in slope - intercept form is y = (- 1/4)x + 2.